On spectrums of certain harmonic functions attached to the Riemann zeta-function

A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.     

Maximum likelihood estimate for discontinuous parameter in stochastic hyperbolic systems

The purpose of this paper is to study the identification problem of a spatially varying discontinuous parameter in stochastic hyperbolic equations. In previous works, the consistency property of the maximum likelihood estimate (MLE) was explored and the generating algorithm for MLE proposed under the condition that an unknown parameter is in a sufficiently regular space with respect to spatial variables.In order to show the consistency property of the MLE for a discontinuous coefficient, we use the method of sieves, i.e. the admissible class of unknown parameters is projected into a finite-dimensional space. For hyperbolic systems, we cannot obtain a regularity property of the solution with respect to a parameter. So in this paper, the parabolic regularization technique is used. The convergence of the derived finite-dimensional MLE to the infinite-dimensional MLE is justified under some conditions.     

Crosslinked poly(N-isopropylacrylamide) gel for electrophoretic separation and recovery of substances

Crosslinked poly(N-isopropylacrylamide) gel was tested on the feasibility for a preparative electrophoretic matrix. Horse heart myoglobin and bovine hemoglobin were well separated on the gel matrix electrophoretically by molecular sieving effect of the gel network. Relative mobilities of those proteins in the gel were larger than those in a crosslinked polyacrylamide gel of the same polymer concentration. After the separation, the protein-containing portion of the gel underwent swelling at 4°C and deswelling at 37°C, alternatively. As a result of the deswelling, each protein was recovered in a discharged solution out of the gel at almost 100% yield.     

Control of the bioluminescence starting time by inoculated cell density.

In this study, we attempted to control the timing of light-emission from bioluminescent bacteria, by changed cell numbers inoculated into medium. Luminous bacteria express bioluminescence when the number of cells reached a threshold. Inoculated cell density had an effect on the time of bioluminescence starting. Samples were prepared by varying cell density of inoculation. In the results, all the vials showed different luminescence profiles in the order of inoculated cell population.     

Thermosensitive biodegradable polydepsipeptide

A poly(N-isopropylacrylamide) (PNIPAAm)-like biodegradable thermosensitive polydepsipeptide, poly[Glc-Asn(N-isopropyl)], was synthesized by introducing an isopropyl amide group into poly[Glc-Asn]. Poly[Glc-Asn(N-isopropyl)] was degraded in vitro by cleavage of the ester bonds in the main chain in water at room temperature. The non-toxic nature of the polymer and its degradation products, coupled with a cloud point at 29 degrees C in water, make this polymer attractive for biomedical implant applications.     

An intramolecular diels-alder approach to quassinoids—a stereoselective construction of a-aromatic klaineanone

Thermolysis of a benzocyclobutene derivative ($\text{20}$) prepared from norcamphor produced stereoselectively a tetracyclic compound ($\text{2}$), which was converted to a lactone ($\text{21}$) having correct stereochemistry at C₇, C₈, C₉, C₁₁, C₁₃, and C₁₄ positions of (±)-klaineanone.